1 / 22

Characterizing non-equilibrium and radial flow at RHIC with Tsallis statistics

次平衡非广度统计. Zebo Tang ( 唐泽波 ) , Lijuan Ruan, Fuqiang Wang, Gene van Buren, Yichun Xu, Zhangbu Xu. Characterizing non-equilibrium and radial flow at RHIC with Tsallis statistics. Phys. Rev. C 79, 051901(R) (2009). What physics can spectra address?

caden
Download Presentation

Characterizing non-equilibrium and radial flow at RHIC with Tsallis statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 次平衡非广度统计 Zebo Tang (唐泽波), Lijuan Ruan, Fuqiang Wang, Gene van Buren, Yichun Xu, Zhangbu Xu Characterizing non-equilibrium and radial flow at RHIC with Tsallis statistics Phys. Rev. C 79, 051901(R) (2009) What physics can spectra address? Why do we need a new BlastWave model and non-equilibrium How to implement Tsallis statistics in BlastWave framework Can spectra tell us about fluctuation and bulk viscosity? Who said p+p spectra are similar to Au+Au? Summary and Outlook Zhangbu Xu

  2. What physics can Spectra tell us? • Low pT • Integrated particle yields (dN/dy) (chemistry) • Radial Flow and freeze-out temperature • Intermediate pT • Coalescence • High pT • Jet quenching • What are the connections among them • Bulk medium interaction and pressure gradient drives thermalization and radial flow • Thermalization and quark degree of freedom provides quark coalescence • Jet quenching dissipates energy into the system • Bulk Viscosity, Fluctuation? Zhangbu Xu

  3. mT slope vs mass Nu Xu’s plot Nu Xu, QM2008 STAR whitepaper, PRL92(2004) Teff = T+1/2mb2 Zhangbu Xu

  4. Radial flow Spectral shape depends on PID mass Higher mass => larger inverse slope More central => larger inverse slope STAR PRL92 F. Retiere and M. Lisa PRC70; PHENIX PRL88 Zhangbu Xu

  5. Blast Wave 爆炸波 F. Retiere, M. Lisa, PRC70 E. Schnedermann, J. Sollfrank, U. Heinz, nucl-th/9307020, PRC48 (cited 312) Assumptions: Local thermal equilibrium  Boltzmann distribution Longitudinal and transverse expansions (1+2) Radial flow profile (r)Atanh(m(r/R)n ), (n=1) Temperature and <> are global quantities BGBW: Boltzmann-Gibbs Blast-Wave Zhangbu Xu

  6. Limitations of THE BlastWave STAR PRC71 • Strong assumption on local thermal equilibrium • Arbitrary choice of pT range of the spectra (low and high cuts) • Flow velocity <b>=0.2 in p+p • Lack of non-extensive quantities to describe the evolution from p+p to central A+A collisions • example in chemical fits: canonical to grand canonical ensemble • mT spectra in p+p collisions:Levy function or mT power-law • mT spectra in A+A collisions:Boltzmann or mT exponential • What function can capture these features? STAR PRL99 Zhangbu Xu

  7. Tsallis Statistics • Nice web based notebooks: Tsallis Statistics, Statistical Mechanics for Non-extensive Systems and Long-Range Interactions http://www.cscs.umich.edu/~crshalizi/notabene/tsallis.html • http://tsallis.cat.cbpf.br/biblio.htm Negative Binomial Distribution: =1/(q-1) Temperature fluctuation: G. Wilk: arXiv: 0810.2939; C. Beck, EPL57(2002)3 Zhangbu Xu

  8. It is all about the q-statistics • Why is this relevant to us (Heavy-ion physics)? • We have dealt with Boltzmann distributionBut the spectra are clearly non-Boltzmann • It is easy to make a change • It is easy to compare • Change mT exponential to mT power law Zhangbu Xu

  9. Tsallis statistics in Blast Wave model With Tsallis distribution, the BlastWave equation is: Where =Atanh(m(r/R)n), n=1 ; any of the three integrals is HypergeometryF1 : flow velocity Zhangbu Xu

  10. Fit results in Au+Au collisions STAR PRL97 STAR PRL99 STAR PRL98 STAR PRL92 Au+Au 60—80%: <>=0 T = 0.114 +- 0.003 q = 1.086 +- 0.002 chi^2/nDof = 138/ 123 Au+Au 0—10%: <> = 0.470+- 0.009 T = 0.122 +- 0.002 q = 1.018 +- 0.005 chi^2/nDof = 130 / 125 Zhangbu Xu

  11. How is result different from BGBW? Central Au+Au collisions BGBW: underpredict low mass particles at high pt overpredict high mass particles at high pt Peripheral Au+Au collisions BGBW: underpredict low mass particles at high pt underpredict high mass particles at high pt Zhangbu Xu

  12. Dissipative energy into flow and heat More thermalized Decrease of q1, closer to Boltzmann Increase of radial flow (00.5) Increase of temperature T,  (q-1)2, NOT linear (q-1) Zhangbu Xu

  13. Related to bulk viscosity () cp, and a are, respectively, the specific heat under constant pressure, density and the coefficient of external conductance G. Wilk: arXiv: 0810.2939 Zhangbu Xu

  14. Results in p+pcollisioins STAR PLB615 STAR PLB637 STAR PLB612 STAR PLB616 STAR PRC72 STAR PRC75 <> = 0 T = 0.0889+- 0.004 q = 1.100 +- 0.003 chi^2/nDof = 53 / 66 <> = 0 T = 0.097+- 0.010 q = 1.073 +- 0.005 chi^2/nDof = 55 / 73 Zhangbu Xu

  15. How is result different from BGBW? BGBW: underpredicts higher pt yields for all mesons in p+p Baryons and mesons are created differently in p+p: baryons from gluons and popcorn model? Zhangbu Xu

  16. Evolution from p+p to Au+Au • Sharp increase of <T> from p+p to peripheral Au+Au • Similar q from p+p to peripheral Au+Au • Radial flow is zero at p+p and peripheral Au+Au Zhangbu Xu

  17. Baryon and meson are different classes STAR PRC75 In p+p collisions, the mT spectra of baryons and mesons are in two groups Maybe we should not call p+p system as a whole global system However, equilibrated toward more central Au+Au collisions Zhangbu Xu

  18. Observations from the q-statistics • Fit spectra well for all particles with pT<~ 3 GeV/c • Radial flow increases from 0 to 0.5c • Kinetical freeze-out temperature increases from 90 (110) to 130 MeV • q-1 decreases from 0.1 to 0.01 • T and b depend on (q-1)2 • p+p collisions are very different, split between mesons and baryons • Tsallis statistics describes the data better than Boltzmann-Gibbs statistics • Radial flow is zero in p+p and peripheral Au+Au collisions • Evolution from peripheral to central Au+Au collisions: hot spots (temperature fluctuation) are quenched toward a more uniform Boltzmann-like distribution • dissipative energy into heat and flow, related to bulk viscosity • Energy conservation is a built-in requirement in any statistical model (that is where you get the temperature) Zhangbu Xu

  19. Outlook • Search for critical point: • large bulk viscosity at phase transition • PID spectra to 3 GeV/c • Study T, bvs q-1 with centrality and energyAGSSPSRHIC • Abnormal larger (small) coefficients of T (b) vs (q-1)2 • Higher energy at LHC: • Large power-law tail due to semi-hard processes • Without Tsallis distribution, it is likely impossible to extract radial flow from spectra • Good (large) non-extensive effect and easy to extract bulk viscosity D. Kharzeev et al., QM08 Zhangbu Xu

  20. Application of Tsallis statistics has a long history at RHIC • mT-m0 power-law • STAR PRD74 (2006) • STAR PRC71 (2005) • STAR PRL99 (2007) • Energy conservationZ. Chajecki and M. Lisa arXiv:0807.3569 • Soft+MinijetsT. Trainor, arXiv:0710.4504 Zhangbu Xu

  21. 作业题 I 1）证明： 2) 证明:

  22. 作业题 II 1）证明：

More Related